How to change the pattern of a texture for each tile in a shader?
In order to make each 'tile' different you need to change the 'noise' used to generate the pattern to be different for each tile. For your texture you are using a Brick texture to generate the 'tiles' - the Brick texture produces two outputs - the Factor and the Color of each 'brick'. Since the Color is consistent over each whole 'brick' - and is random for each brick (a random mix between the two supplied colors) - we can use this to generate a unique 'brick id' for each 'brick'.
The 'brick id' can be used to offset the Noise texture used for your texture by a different amount per 'tile' so as to generate a different pattern.
For example, I have tried to mimic your setup from your image (I think it's fairly close) and have added the highlighted nodes to adjust the texture per 'tile' :

Note the Brick Texture node set to the same values as the one used to generate the tiles. Color1 and Color2 are set to wildly different values to generate a large range of randomness.
The Color is passed to a Multiply node to increase the 'distance' of each random identifier (to increase the amount of difference in the noise) which is then used as the Z-coordinate of the Vector used to generate the noise.
This can produce the following results :

Blend file included